In a pushbutton tuner, it is essential to achieve a desired selection or tuning operation simply by depressing a push button. To satisfy this requirement, there have been proposed various mechanisms. On the other hand, where the pushbutton tuner is used in automobiles as a car equipment, it should be compact, especially thin to be suitably assembled with other equipment and mounted within a limited space effectively. Various structures have been proposed to reduce a thickness of the pushbutton tuner. In general, a desired structure to reduce the thickness of the pushbutton tuner is such that the button slides are arranged in a plane parallel with a baseplate and link members are also arranged in a plane parallel with the baseplate so as to be operated by setting members provided on the button slides. More specifically, a plurality of link members are crossingly arranged in relation with a pin of each of the setting members and free ends of the link members are rotatable upon retreat of the setting pin to displace a memory slide. The inventors of the present invention have also proposed heretofore this type of structures suitable for an automobile car pushbutton tuner of a reduced thickness. In fact, this type of the structure, wherein crossingly arranged link members are employed, is generally desirable to reduce the thickness of the tuner. However, the structure needs at least two link members for each button slide and accordingly the number of components are inevitably large. In addition, a line drawn between a portion where the link member is pivotally connected to the baseplate and a portion where the link member is pivotally connected to the memory slide crosses a direction of retreat of the memory pin. In other words, since the free ends of the link members, whose base ends are pivotally connected to the baseplate on opposite sides of the respective button slide, are crossed and overlap each other in a direction of retreat of the memory pin, there is a considerable loss in force for displacement of the memory slide by a component force of the pushing force of the memory pin as can be understood from analysis of trignometry when the mechanism is viewed from above the same. Therefore, there has been proposed a slot on the link member of arcuate shape which receives the merory slide pin. This can overcome the disadvantage of the loss in the operating force, but causes another disadvantage of turning error.